When James Caan is first seen lighting his cigarette, he uses a pack of safety matches, which has its striker on the back of the matches. These were not introduced until c. 1970. In 1963, he would have used matches where the striker is on the front of the matchbook.
The movie is set in 1963. When James Caan is thrown in jail, early on in the movie, the other inmates are singing "The Times They Are a-Changin". He may have sung it on Oct 26th at Carnegie Hall but it wasn't issued until the album, of which it was title track, came out in January, 1964.
While Marlowe is talking to Muffy in his apartment, the newspaper article on the coffee table keeps changing position without being touched - alternatively jumping on and off the envelope and the table.